library(faraway)
data(savings)
savings
g <- lm(sr ~ pop15 + pop75 + dpi + ddpi, savings)
summary(g)
g <- lm(sr ~ pop15 + pop75 + dpi + ddpi, savings)
(tss <- sum((savings$sr-mean(savings$sr))^2))
(rss <- deviance(g))
df.residual(g)
(fstat <- ((tss-rss)/4)/(rss/df.residual(g)))
1-pf(fstat,4,df.residual(g))
g2 <- lm(sr ~ pop75 + dpi + ddpi, savings)
(rss2 <- deviance(g2))
(fstat <- (deviance(g2)-deviance(g))/(deviance(g)/df.residual(g)))
1-pf(fstat,1,df.residual(g))
sqrt(fstat)
(tstat <- summary(g)$coef[2,3])
2*(1-pt(sqrt(fstat),45))
anova(g2,g)
g3 <- lm(sr ~ pop15+dpi , savings)
anova(g3,g)
g <- lm(sr ~ .,savings)
gr <- lm(sr ~ I(pop15+pop75)+dpi+ddpi,savings)
anova(gr,g)
gr <- lm(sr ~ pop15+pop75+dpi+offset(0.5*ddpi),savings)
anova(gr,g)
(tstat <- (0.409695-0.5)/0.196197)
2*pt(tstat,45)
tstat^2
g <- lm(sr ~ pop75+dpi,savings)
summary(g)
gs <- summary(g)
gs$fstat
fstats <- numeric(4000)
for(i in 1:4000){
ge <- lm(sample(sr) ~ pop75+dpi,data=savings)
fstats[i] <- summary(ge)$fstat[1]
}
length(fstats[fstats > 2.6796])/4000
summary(g)$coef[2,3]
tstats <- numeric(4000)
for(i in 1:4000){
ge <- lm(sr ~ sample(pop75) + dpi, savings)
tstats[i] <- summary(ge)$coef[2,3]
}
mean(abs(tstats) > 1.6783)
g <- lm(sr ~ ., savings)
qt(0.975,45)
c(-1.69-2.01*1.08,-1.69+2.01*1.08)
c(0.41-2.01*0.196,0.41+2.01*0.196)
confint(g)
library(ellipse)
plot(ellipse(g,c(2,3)),type="l",xlim=c(-1,0))
points(0,0)
points(coef(g)[2],coef(g)[3],pch=18)
abline(v=confint(g)[2,],lty=2)
abline(h=confint(g)[3,],lty=2)
cor(savings$pop15,savings$pop75)
summary(g,corr=TRUE)$corr
g <- lm(Species ~ Area+Elevation+Nearest+Scruz+Adjacent,gala)
x0 <- c(1,0.08,93,6.0,12.0,0.34) 
(y0 <- sum(x0*coef(g)))
qt(0.975,24)
x <- model.matrix(g)
xtxi <- solve(t(x) %*% x)
(bm <- sqrt(x0 %*% xtxi %*% x0) *2.064 * 60.98)
c(y0-bm,y0+bm)
bm <- sqrt(1+x0 %*% xtxi %*% x0) *2.064 * 60.98
c(y0-bm,y0+bm)
x0 <- data.frame(Area=0.08,Elevation=93,Nearest=6.0,Scruz=12,Adjacent=0.34)
str(predict(g,x0,se=TRUE))
predict(g,x0,interval="confidence")
predict(g,x0,interval="prediction")
grid <- seq(0,100,1)
p <- predict(g,data.frame(Area=0.08,Elevation=93,Nearest=grid,Scruz=12,Adjacent=0.34),se=T,interval="confidence")
matplot(grid,p$fit,lty=c(1,2,2),type="l",xlab="Nearest",ylab="Species")
rug(gala$Nearest)
data(odor)
odor
x <- as.matrix(cbind(1,odor[,-1]))
t(x) %*% x
g <- lm(odor ~ temp + gas + pack, odor)
summary(g,cor=T)
g <- lm(odor ~ gas + pack, odor)
summary(g)
g <- lm(sr ~ pop15 + pop75 + dpi + ddpi, savings)
summary(g)
g <- update(g, . ~ . - pop15)
summary(g)
g <- lm(sr ~ pop15 + pop75 + dpi + ddpi, savings)
summary(g)
g2 <- lm(sr ~ pop75 + dpi + ddpi, savings)
summary(g2)
g3 <- lm(sr ~ pop75 + ddpi, savings)
summary(g3)
g4 <- lm(sr ~ pop75, savings)
summary(g4)
x0 <- data.frame(pop15=32,pop75=3,dpi=700,ddpi=3)
predict(g,x0)
predict(g2,x0)
predict(g3,x0)
predict(g4,x0)